Exemplary embodiments of the present invention relate to a method for direction finding by means of monopulse formation with the aid of a radar system with electronically controlled group antenna and analog beam formation of sum and difference channels.
Electronically controllable group antennas (“phased array antennas”) comprise a linear or planar arrangement of a multiplicity of individual antenna elements with wide aperture angle that can be individually adjusted for their amplitude occupancy and phase occupancy and, when combined, produce a bundled antenna diagram (See, for example, Merrill Skolnik: Radar Handbook, 2nd edition; McGraw-Hill Book Company, Singapore, 1980). The viewing direction is adjusted by the phase occupancy, while the side lobe characteristic is defined by the amplitude occupancy (taper).
The output signals of the individual elements are usually physically added by high frequency antenna splitters (“combiners”), and to supply the output signal of the group antenna. The sum and difference diagrams for monopulse bearing measurement are formed by halving the total aperture and combining the sum signals of the halves in the so-called monopulse combiner at separate outputs with the same and opposite signs. The amplitude occupancy is, therefore, necessarily identical for the sum and difference diagrams.
The monopulse discriminant
                    r        =                  Im          ⁢                      {                          Δ              ∑                        }                                              (        1        )            can be formed as basis for the monopulse bearing measurement from the signal of the sum antenna Σ and that of the difference antenna Δ.
For the two-dimensional case, the aperture is divided into horizontal (x-) and vertical (y-) directions, which leads to the two difference signals Δx and Δy, which yield the monopulse discriminants
                                          r            x                    =                      Im            ⁢                          {                                                Δ                  x                                ∑                            }                                      ⁢                                  ⁢                              r            y                    =                      Im            ⁢                          {                                                                    Δ                    ⁢                                                                                                  y                                ∑                            }                                                          (        2        )            for horizontal and vertical direction finding.
Assuming identical antenna diagrams of the aperture halves, the bearing values in u- and v-coordinates are yielded therefrom in the form of the angular offsets δu, δu of the antenna viewing direction in accordance with
                                          δ            ⁢                                                  ⁢            u                    =                                    2                                                k                  0                                ⁢                                  d                  x                                                      ·                          arctan              ⁡                              (                                  r                  x                                )                                                    ⁢                                  ⁢                              δ            ⁢                                                  ⁢            v                    =                                    2                                                k                  0                                ⁢                                  d                  y                                                      ·                                          arctan                ⁡                                  (                                      r                    y                                    )                                            .                                                          (        3        )            
In this case, the wavenumber at the radar operating frequency f0, is denoted by k0=2πf0/c0, dx and dy, are the phase center spacings of the respective aperture halves in horizontal and vertical directions.
In practice, the partial apertures do not have identical diagrams, but equation 3 constitutes a very good approximation in the region of the main lobe of the sum diagram, as long as it is possible to carry out a symmetrical division of the apertures (for example rectangular, circular or elliptical planar antennas). The useful bearing range typically extends to a drop of approximately 12 dB of the main lobe.
The functional relationship between δu, δv, and rx, ry is denoted as monopulse characteristic. In order to determine small offsets about the antenna viewing direction, the latter is frequently linearized with the slopes in the zero crossing in u- and v-directions in accordance with
                                          m            u                    =                      2                                          k                0                            ⁢                              d                x                                                    ⁢                                  ⁢                              m            v                    =                      2                                          k                0                            ⁢                              d                y                                                                        (        4        )            
The positions x(n), y(n) of the phase centers of the partial apertures are determined by forming the centroid over all individual elements of which the respective aperture half is composed (with nε{r, l, o, u} for the right, left, upper and lower halves). The phase center coordinates are calculated as
                                          x                          (              n              )                                =                                                    ∑                v                            ⁢                                                x                                      e                    ,                    v                                                        (                    n                    )                                                  ·                                  g                                      e                    ,                    v                                                        (                    n                    )                                                                                                      ∑                v                            ⁢                              g                                  e                  ,                  v                                                  (                  n                  )                                                                    ⁢                                  ⁢                              y                          (              n              )                                =                                                    ∑                v                            ⁢                                                y                                      e                    ,                    v                                                        (                    n                    )                                                  ·                                  g                                      e                    ,                    v                                                        (                    n                    )                                                                                                      ∑                v                            ⁢                              g                                  e                  ,                  v                                                  (                  n                  )                                                                                        (        5        )            from the coordinates xe,v(n), ye,v(n) and the amplitude weightings ge,v(n) of the individual elements of a partial aperture, from which, finally, the phase center spacings of the horizontal and vertical aperture halves are yielded as:dx=x(r)−x(t) dy=y(o)−y(u)  (6)
It follows that all the variables are known for carrying out conventional monopulse bearing measurement from the sum signal and the difference signals of an ideal (error free) group antenna.
Deviations from the ideal aperture occupancy—in particular, symmetry errors—lead to bearing errors. Deterministic causes of such deviations are, for example, individual failed elements or entire groups of elements (rows, planks, slats).
The (systematic) monopulse bearing error {εu, εv} can be ascertained by calculating the bearing {δu,δv} in accordance with equation 3 at arbitrary positions {u,v} in the monopulse definition range about the antenna viewing direction {uant,vant} and determining the difference with respect to the actual position in u and v:εu=u−uant−δu εv=v−vant−δv  (7)
Here, the values of the corresponding antenna diagrams in the direction {u,v} are to be substituted for Σ, Δx, and Δy. In the noise-free case, these are identical to the signals that supply the antenna for an incident wavefront from direction {u,v}.
The absolute value of the total bearing error amounts toε=√{square root over (εu2+εv2)}  (8)
The effect of errors on the aperture occupancy is illustrated by way of example with the aid of the simulation of a two-dimensional, circular group antenna with 1000 elements in the X-band, which are arranged in a triangular array. FIG. 1 visualizes position and amplitudes of the individual elements in a normalized linear scale. An occupancy that drops toward the edge to −15 dB (approximately 0.2) is undertaken for side lobe reduction. It may be assumed that the aperture is composed structurally of vertical half lines, of which four are blank, giving rise to symmetry errors in the horizontal and vertical directions.
Magnitude errors of the monopulse bearing measurement in accordance with equations 3 to 8 inside the bearing range are illustrated as encoded in gray levels in FIG. 2 and FIG. 3. Adopted here as limit of the bearing range is the 6 dB drop of the sum diagram, which for this antenna describes approximately a circle of radius 0.05 about the viewing direction (here: {uant,vant}) in the u/v plane. This range comprises approximately half the entire main lobe width, or 1.5 times the 3 dB lobe width.
Only slight deviations at the edge of the range can be established for the error-free aperture occupancy (FIG. 2). They reach a maximum value of 3% with reference to the maximum bearing value. Assuming aperture errors (FIG. 3), the maximum bearing error rises substantially up to 15%.
Bearing errors are tolerated within certain limits in relation to the current prior art for radar systems with electronically swiveled group antennas whose sum and difference diagrams are analogously formed.
In the general case of a group antenna, the sum and difference diagrams are not, as described above, formed by combination on the high frequency side (physical, analog), but the received signals of the individual elements are firstly available individually. After they have been digitized, it is then possible to carry out arbitrary beam shaping, and thus also monopulse bearing measurement, digitally (digital beam forming, DBF), by multiplying and adding up the element signals numerically with complex weighting factors. Although this does require a substantially greater outlay on hardware for the antenna, the result nevertheless is many degrees of freedom in configuring their properties.
With regard to the monopulse calculation, the limitation that sum and difference diagrams are formed with one and the same amplitude occupancy is abolished, and so optimal solutions are possible here. On the basis of the maximum likelihood estimate (MLE), weighting factors are found for forming the sum and difference diagrams in which it is also possible to take account of deviations from the idealized antenna aperture. An example of this is thinned arrays.
The algorithms and various aspects of such a generalized monopulse are described, for example, in Ulrich Nickel: Overview of Generalized Monopulse Estimation; IEEE A&E Systems Magazine, Vol. 21, No. 6, June 2006, Part 2: Tutorials, pp. 27-56.
The fundamental idea of the generalized monopulse according to the Nickel article consists in determining adapted monopulse bearing values δuad and δuad from the monopulse discriminants (equation 2) of the faulty antenna by means of an affine mapping (simple displacement and linear transformation). This is described in the form of a linear equation system:
                              (                                                                      δ                  ⁢                                                                          ⁢                                      u                    ad                                                                                                                        δ                  ⁢                                                                          ⁢                                      v                    ad                                                                                )                =                  C          ·                      (                                                                                                      r                      x                                        -                                          μ                      x                                                                                                                                                              r                      y                                        -                                          μ                      y                                                                                            )                                              (        9        )            
Slope and bias of the monopulse bearing measurement in the antenna viewing direction are thereby adapted to the real conditions.
The correction terms C and μx,y are derived from the requirements that in the viewing directionδuad(uant,vant)=0δvad(uant,vant)=0  (10)must hold, as must
                                          (                                                                                                                              ∂                        δ                                            ⁢                                                                                          ⁢                                              u                        ad                                                                                    ∂                      u                                                                                                                                                          ∂                        δ                                            ⁢                                                                                          ⁢                                              u                        ad                                                                                    ∂                      v                                                                                                                                                                                      ∂                        δ                                            ⁢                                                                                          ⁢                                              v                        ad                                                                                    ∂                      u                                                                                                                                                          ∂                        δ                                            ⁢                                                                                          ⁢                                              v                        ad                                                                                    ∂                      v                                                                                            )                    ⁢                      |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            (                                                                  u                        ant                                            ,                                              v                        ant                                                              )                                                                                      =                  (                                                    1                                            0                                                                    0                                            1                                              )                                    (        11        )            for the partial derivatives (slopes) thereof.
This approach includes the simplified assumption of a linearization about the point of the viewing direction, something which then facilitates a closed solution for C and μx,y as a function of the variables describing the antenna. The derivation and general solution (in vector notation) are described in the Nickel article.
The application of the generalized monopulse according to the Nickel article is, however, not suitable for the correction of moderate aperture errors. In particular, the linearization undertaken in its formulation according to equation 9 leads, for relatively large offsets of the antenna viewing direction, to errors that are larger than those typically caused by failed antenna elements.
Exemplary embodiments of the present invention are directed to obtaining a bearing with high accuracy when applying monopulse bearing measurement on a group antenna with analog beam shaping of sum and difference diagrams even given a disturbed aperture occupancy of the antenna.
The concept of the generalized monopulse known from the prior art is modified in accordance with the invention in order to take account of previously known deviations in the aperture occupancy from the ideal case during monopulse calculation, even given group antennas with analog beam shaping of sum and difference channels.
It is often known in a total radar system, from cyclically conducted self-tests (health check, built-in tests, for example in the case of each system start), which elements of the antenna receiving aperture (individual elements or planks or slats) have failed. This information is used in accordance with the invention in order to calculate an error-corrected monopulse bearing measurement.
Moreover, known amplitude and phase errors of the receiving elements can also be involved in the correction.
However, structural deviations in the antenna aperture from the ideal case of symmetrical divisibility (for example in relation to the implementation of structurally conformal antennas) are known from the start and can be taken into account in the correction.
An extended maintenance-free operation of the group antenna can be ensured by means of the invention without having to decrease the bearing accuracy.